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At least 289 records · Page 16
All sourcesNASA NTRSDOE OSTI
NASA NTRS1977

An approximate calculation of the strong interaction on a transonic airfoil

This paper describes an interactive computational scheme that calculates the transonic flow field over an airfoil. The inviscid flow, the turbulent boundary layer in the weak interaction region, and the elliptic flow in the strong interaction region are computed separately, and the solutions are matched iteratively in a direct, second-order interaction scheme. The pressure distribution, obtained from a transonic, small-perturbation solution, is prescribed on the boundary layer and the Navier-Stokes equations and the ensuing displacement thicknesses are used to modify the inviscid flow. The best overall results are obtained by using a turbulence model that eliminates the eddy viscosity in the strong interaction region. Computed pressure distributions are compared with experimental data and with Navier-Stokes solutions. In weak interactions, the agreement with experimental data is very good, as it is also in strong interactions except for the pressures in the separated-flow region. There the agreement is qualitative only, and the pressure recovery is too high. The results in both cases are superior or equal to those of the Navier-Stokes solutions, and the present method is significantly faster.

Seginer, A.↗
NASA NTRS1976

Recent computation of viscous effects in transonic flow

The paper describes some improvements to a method of solving the time-dependent Reynolds-averaged Navier-Stokes equations for two-dimensional compressible flows for describing the coupling between viscous and inviscid regions in transonic flows. Mesh patching is implemented at the sublayer-boundary layer interfaces and the boundary layer-inviscid flow interface. Mesh stretching is geometric and is small in regions of large gradients and large in regions of small gradients, thus preserving second-order accuracy. Mesh lines are arranged so as to accommodate MacCormack's rapid solver for hyperbolic systems and a wider class of turbulent transport models. Results of computations of transonic flows over lifting airfoils are compared with experimental data and other solutions.

Deiwert, G. S.↗
NASA NTRS1977

The low-latitude circulation of Mars

A steady-state two-layer atmospheric model is used in an attempt to simulate the circulation of the equatorial regions of Mars, with consideration of both thermal and mechanical orographic effects. A steady-state solution is sought with the aim of producing mean seasonal circulations upon which tides can be superimposed, and the relative importance of orographic forcing at low latitudes is evaluated. It is assumed that the atmospheres over a topographic feature and over flat terrain possess the same radiative and convective properties, simple dissipation laws are introduced which represent a surface drag effect, and six first-order difference equations are obtained and then reduced to two linear complex second-order coupled difference equations. Analysis of the response of the equinoctial basic wind field to a Gaussian orographic feature situated at the equator and zero deg longitude reveals a number of similarities and differences between the Martian and terrestrial responses. Most of the similarities are explained in terms of the dynamics of a rotating atmosphere, while the major differences are at least partially explained by the different optical properties, lower boundaries, and smaller mass of the Martian atmosphere.

Webster, P. J.↗
NASA NTRS1977

On the gravitational potential and field anomalies due to thin mass layers

The gravitational potential and field anomalies for thin mass layers are derived using the technique of matched asymptotic expansions. An inner solution is obtained using an expansion in powers of the thickness and it is shown that the outer solution is given by a surface distribution of mass sources and dipoles. Coefficients are evaluated by matching the inner expansion of the outer solution with the outer expansion of the inner solution. The leading term in the inner expansion for the normal gravitational field gives the Bouguer formula. The leading term in the expansion for the gravitational potential gives an expression for the perturbation to the geoid. The predictions given by this term are compared with measurements by satellite altimetry. The second-order terms in the expansion for the gravitational field are required to predict the gravity anomaly at a continental margin. The results are compared with observations.

Ockendon, J. R.↗
NASA NTRS1976

Comparison of impact basins on Mercury, Mars and the moon

The statistics of basins on the moon, Mercury, and Mars are compared. The basic similarities of basins on Mars, Mercury, and the moon argue convincingly that they result from the same processes. Variations in onset diameters and relative abundances, however, suggest that these basic processes are modulated by second-order factors.

Wood, C. A.↗
NASA NTRS1977

A critical study of higher-order numerical methods for solving the boundary-layer equations

A fourth-order box method is presented for calculating numerical solutions to parabolic, partial differential equations in two variables or ordinary differential equations. The method is the natural extension of the second-order Keller Box Scheme to fourth order and is demonstrated with application to the incompressible, laminar and turbulent boundary-layer equations. The efficiency of the present method is compared with other two-point and three-point higher-order methods; namely, the Keller Box Scheme with Richardson extrapolation, the method of deferred corrections, and the three-point spline methods. For equivalent accuracy, numerical results show the present method to be more efficient than the other higher-order methods for both laminar and turbulent flows.

Wornom, S. F.↗
NASA NTRS1976

The linear quadratic optimal control problem for infinite dimensional systems over an infinite horizon - Survey and examples

Available published results are surveyed for a special class of infinite-dimensional control systems whose evolution is characterized by a semigroup of operators of class C subscript zero. Emphasis is placed on an approach that clarifies the system-theoretic relationship among controllability, stabilizability, stability, and the existence of a solution to an associated operator equation of the Riccati type. Formulation of the optimal control problem is reviewed along with the asymptotic behavior of solutions to a general system of equations and several theorems concerning L2 stability. Examples are briefly discussed which involve second-order parabolic systems, first-order hyperbolic systems, and distributed boundary control.

Bensoussan, A.↗
NASA NTRS1977

Isothermal degradation of poly-2,2'-/m-phenylene/-5,5'-bibenzimidazole

The isothermal degradation of poly-2,2'-(m-phenylene)-5,5'-bibenzimidazole in vacuo has been studied. Measurement of the increase in pressure with time, coupled with infrared analysis, was used to determine the distribution of the degradation products. Processes A and B with different second-order rate laws were determined to be significant in the temperature range of 550-700 C. Process A leads to the formation of equimolar quantities of hydrogen and ammonia and has an activation energy of 68 kcal/mole. Process B leads to the production of HCN, NH3, and H2 in the ratio of 1:1:2.5 and has an activation energy of 77 kcal/mole. The activation energies and the rate laws are consistent with a mechanism in which the initial degradation step is the bimolecular reaction of two aromatic rings.

Lerner, N. R.↗
NASA NTRS1977

Effect of flow on quasi-one-dimensional acoustic wave propagation in a variable area duct of finite length

The general equation for the velocity potential of quasi-one-dimensional acoustic wave motion in a variable area, finite duct with one-dimensional flow is derived by using a perturbation technique. The nonlinear second-order partial differential equation is linearized and then solved, by either a power series expansion method or the Runge-Kutta fourth-order method, for harmonic time dependence. The boundary condition taken at the duct mouth is that of matching the impedance of the duct sound field to that of the radiation field at the duct opening. Three axial Mach number variations along the duct axis are considered and the results obtained are compared with those for the case of constant Mach number, to determine the influence of the axial velocity gradient on sound propagation. The effect of flow on the radiation impedance is also considered.

Lumsdaine, E.↗
NASA NTRS1977

Numerical determination of the fundamental eigenvalue for the Laplace operator on a spherical domain

Methods for obtaining approximate solutions for the fundamental eigenvalue of the Laplace-Beltrami operator (i.e., the membrane eignevalue problem for the vibration equation) on the unit spherical surface are developed. Two types of spherical surface domains are considered: the interior of a spherical triangle, and the exterior of a great circle arc extending for less than pi radians (a spherical surface with a slit). In both cases, zero boundary conditions are imposed. In order to solve the resulting second-order elliptic partial differential equations in two independent variables, a finite difference approximation is employed. The fundamental eigenvalue is approximated by iteration utilizing the power method and point successive overrelaxation. Some numerical results are given and compared, in certain special cases, with analytical solutions to the eigenvalue problem. The significance of the numerical eigenvalue results is discussed in terms of the singularities in the solution of three-dimensional boundary-value problems near a polyhedral corner of the domain.

Walden, H.↗
NASA NTRS1977

Turbulent transport model of a thunderstorm gust front

A second-order closure turbulent model is adopted to predict complex fluid flows; few a priori assumptions about the internal turbulent and mean flow structures are required. The flow simulations are applied to the analysis of local gust fronts generated by rain-cooled outflows from severe thunderstorms. Results of the simulations provide a means for discussing the behavior of an aircraft passing through a thunderstorm-related downdraft.

Teske, M. E.↗
NASA NTRS1976

Polynominal Interpolation Methods for Viscous Flow Calculations

Higher-order collocation procedures resulting in tridiagonal matrix systems are derived from polynomial spline interpolation and by Hermitian (Taylor series) finite-difference discretization. The similarities and special features of these different developments are discussed. The governing systems apply for both uniform and variable meshes. Hybrid schemes resulting from two different polynomial approximations for the first and second derivatives lead to a nonuniform mesh extension of the so-called compact or Pad? difference technique (Hermite 4). A variety of fourth-order methods are described and the Hermitian approach is extended to sixth-order (Hermite 6). The appropriate spline boundary conditions are derived for all procedures. For central finite differences, this leads to a two-point, second-order accurate generalization of the commonly used three-point end-difference formula. Solutions with several spline and Hermite procedures are presented for the boundary layer equations, with and without mass transfer, and for the incompressible viscous flow in a driven cavity. Divergence and nondivergence equations are considered for the cavity. Among the fourth-order techniques, it is shown that spline 4 has the smallest truncation error. The spline 4 procedure generally requires one-quarter the number of mesh points in a given coordinate direction as a central finite-difference calculation of equal accuracy. The Hermite 6 procedure leads to remarkably accurate boundary layer solutions.

Rubin, S. G.↗
NASA NTRS1952

Preliminary Investigation of Cyclic De-Icing of an Airfoil Using an External Electric Heater

An investigation was conducted in the NACA Lewis icing research tunnel to determine the characteristics and requirements of cyclic deicing of a 65,2-216 airfoil by use of an external electric heater. The present investigation was limited to an airspeed of 175 miles per hour. Data are presented to show the effects of variations in heat-on and heat-off periods, ambient air temperature, liquid-water content, angle of attack, and. heating distribution on the requirements for cyclic deicing. The external heat flow at various icing and heating conditions is also presented. A continuously heated parting strip at the airfoil leading edge was found necessary for quick, complete, and consistent ice removal. The cyclic power requirements were found to be primarily a function of the datum temperature and heat-on time, with the other operating and meteorological variables having a second-order effect. Short heat-on periods and high power densities resulted in the most efficient ice removal, the minimum energy input, and the minimum runback ice formations. The optimum chordwise heating distribution pattern was found to consist of a uniform distribution of cycled power density in the impingement region. Downstream of the impingement region the power density decreased to the limits of heating which, for the conditions investigated, extended from 5.7 percent chord on the upper surface of the airfoil to 8.9 percent chord on the lower surface. Ice removal did not take place at a heater surface temperature of 32 F; surface temperatures of approximately 50 to 100 F were required to effect removal. Better de-icing performance and greater energy savings would be possible with a heater having a higher thermal efficiency.

Lewis, James P.↗
NASA NTRS1953

Theoretical pressure distribution and wave drags for conical boattails

Afterbody pressure distributions and wave drag were calculated using a second-order theory for a variety of conical boattails at zero angle of attack. Results are presented for Mach numbers from 1.5 to 4.5, area ratios from 0.200 to 0.800, and boattail angle from 3 degrees to 11 degrees. The results indicate that for a given boattail angle, the wave drag decreases with increasing Mach number and area ratio. The wave drag, for a constant area ratio, increases with increasing boattail angle. For a specific Mach number, area ratio, and fineness ratio, a comparison of the wave-drag coefficients for conical, tangent-parabolic, and secant-parabolic boattails showed the conical boattail to have the smallest wave drag.

Jack, John R↗
NASA NTRS1954

Aerodynamics of Slender Bodies at Mach Number of 3.12 and Reynolds Numbers from 2 x 10(exp 6) to 15 x 10(exp 6) IV : Aerodynamic Characteristics of Series of Four Bodies Having Near-parabolic Noses and Cylindrical Afterbodies

Pressure distributions and forces for a series of four bodies of revolution having nose-fineness ratios varying from 4 to 10 have been obtained and compared with theory for a Mach number of 3.12, a Reynolds number range of 2x10(sup)6 to 14x10(sup)6, and angles of attack from zero to 9 degrees. In general, a comparison of the experimental data with a second-order theory showed good agreement for the range of variables investigated.

BODIES - FITNESS RATIO↗
NASA NTRS1954

Aerodynamics of Slender Bodies at Mach Number of 3.12 and Reynolds Numbers from 2 x 10(exp 6) to 15 x 10(exp 6) V : Aerodynamic Load Distributions for a Series of Four Boattailed Bodies

Pressure distributions for a series of four boattailed bodies of revolution were obtained and compared with theory for a Mach number of 3.12, a Reynolds number range of 2 x 10 to 6th power to 14 x 10 to the 6th power, and angles of attack from zero to 9 degrees. Second-order theory adequately predicted the pressure distribution for regions free of the effects of cross-flow separation.

Moskowitz, Barry↗
NASA NTRS1956

An analog study of a shock-position diffuser control on a supersonic turbojet engine

Shock position was assumed to be controlled by air bleed through a diffuser-exit bypass door operated by a second-order servomotor. Pressure disturbance resulting from changes in bypass-door position had whereas a disturbance in engine speed had a large effect on diffuser pressure and could impose severe requirements on diffuser control response. The controlled diffuser response improved with faster servomotor response and smaller diffuser dead time and lag. The effect of diffuser dead time on diffuser response was greater than the effect of diffuser lag.

Novik, David↗
NASA NTRS1958

Investigation of a Nonlinear Control System

A discontinuous variation of coefficients of the differential equation describing the linear control system before nonlinear elements are added is studied in detail. The nonlinear feedback is applied to a second-order system. Simulation techniques are used to study performance of the nonlinear control system and to compare it with the linear system for a wide variety of inputs. A detailed quantitative study of the influence of relay delays and of a transport delay is presented.

Flugge-Lotz, I↗